arXiv Open Access 2021

Stably diffeomorphic manifolds and the realisation of modified surgery obstructions

Anthony Conway Diarmuid Crowley Mark Powell Joerg Sixt

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Abstrak

For every $k \geq 2$ we construct infinitely many $4k$-dimensional manifolds that are all stably diffeomorphic but pairwise not homotopy equivalent. Each of these manifolds has hyperbolic intersection form and is stably parallelisable. In fact we construct infinitely many such infinite sets. To achieve this we prove a realisation result for appropriate subsets of Kreck's modified surgery monoid $\ell_{2q+1}(\mathbb{Z}[π])$, analogous to Wall's realisation of the odd-dimensional surgery obstruction $L$-group $L_{2q+1}^s(\mathbb{Z}[π])$.

Topik & Kata Kunci

math.GT

Penulis (4)

Anthony Conway

Diarmuid Crowley

Mark Powell

Joerg Sixt

Format Sitasi

APA MLA BibTeX

Conway, A., Crowley, D., Powell, M., Sixt, J. (2021). Stably diffeomorphic manifolds and the realisation of modified surgery obstructions. https://arxiv.org/abs/2109.05632

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Informasi Jurnal

Tahun Terbit: 2021
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓